{"paper":{"title":"Input Subspace Detection for Dimension Reduction in High Dimensional Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Paul G. Constantine, Qiqi Wang","submitted_at":"2012-02-16T03:39:10Z","abstract_excerpt":"This manuscript is superseded by Constantine, Dow, and Wang's \"Active Subspaces in Theory and Practice: Applications to Kriging Surfaces\" [SIAM J. of Sci. Comput., 36 (2014), pp. A1500-A1524].\n  Many multivariate functions encountered in practice vary primarily along a few directions in the space of input parameters. When these directions correspond with coordinate directions, one may apply global sensitivity measures to determine the parameters with the greatest contribution to the function's variability. However, these methods perform poorly when the directions of variability are not aligned"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3508","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}